Systems of quotients and Martindale-like quotients of Jordan–Lie triple systems

Abstract

This article is devoted to introducing the definition of systems of quotients of Jordan–Lie triple systems and surveying the vital properties which can be lifted from a Jordan–Lie triple system to systems of quotients of Jordan–Lie triple system. Furthermore, the notions of systems of Martindale-like quotients of a Jordan–Lie triple system with respect to a power filter of sturdy ideals are introduced and the relationship between the systems of quotients of a Jordan–Lie triple system and the systems of Martindale-like quotients of a Jordan–Lie triple system are investigated. What’s more, main propositions about algebras of quotients of δ Jordan–Lie algebras are presented and the relationship between algebras of quotients of Jordan–Lie algebras and systems of quotients of Jordan–Lie triple systems are highlighted. Besides, some connections between systems of Martindale-like quotients of a Jordan–Lie triple system T and algebras of Martindale-like quotients of its standard embedding Jordan algebra L(T) are considered, too.

Keywords:

• Jordan–Lie systems
• Martindale-like quotients
• systems of quotients

2020 Mathematics Subject Classification:

• 17D99
• 17B10

Additional information

Funding

Supported by NNSF of China (Nos. 11771069, 12071405, 12001141, 11801066).